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GCF of 10 and 25

GCF of 10 and 25 is the largest possible number that divides 10 and 25 exactly without any remainder. The factors of 10 and 25 are 1, 2, 5, 10 and 1, 5, 25 respectively. There are 3 commonly used methods to find the GCF of 10 and 25 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 10 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 25?

Answer: GCF of 10 and 25 is 5.

Explanation:

The GCF of two non-zero integers, x(10) and y(25), is the greatest positive integer m(5) that divides both x(10) and y(25) without any remainder.

Methods to Find GCF of 10 and 25

The methods to find the GCF of 10 and 25 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 10 and 25 by Prime Factorization

Prime factorization of 10 and 25 is (2 × 5) and (5 × 5) respectively. As visible, 10 and 25 have only one common prime factor i.e. 5. Hence, the GCF of 10 and 25 is 5.

GCF of 10 and 25 by Long Division

GCF of 10 and 25 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 25 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 10 and 25.

GCF of 10 and 25 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 25: 1, 5, 25

There are 2 common factors of 10 and 25, that are 1 and 5. Therefore, the greatest common factor of 10 and 25 is 5.

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GCF of 10 and 25 Examples

Example 1: For two numbers, GCF = 5 and LCM = 50. If one number is 25, find the other number.

Solution:

Given: GCF (x, 25) = 5 and LCM (x, 25) = 50
∵ GCF × LCM = 25 × (x)
⇒ x = (GCF × LCM)/25
⇒ x = (5 × 50)/25
⇒ x = 10
Therefore, the other number is 10.
Example 2: The product of two numbers is 250. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 250
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 250/5
Therefore, the LCM is 50.
Example 3: Find the GCF of 10 and 25, if their LCM is 50.

Solution:

∵ LCM × GCF = 10 × 25
⇒ GCF(10, 25) = (10 × 25)/50 = 5
Therefore, the greatest common factor of 10 and 25 is 5.

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FAQs on GCF of 10 and 25

What is the GCF of 10 and 25?

The GCF of 10 and 25 is 5. To calculate the greatest common factor (GCF) of 10 and 25, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 10 and 25, i.e., 5.

How to Find the GCF of 10 and 25 by Prime Factorization?

To find the GCF of 10 and 25, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 25 = 5 × 5.
⇒ Since 5 is the only common prime factor of 10 and 25. Hence, GCF (10, 25) = 5.
☛ What are Prime Numbers?

How to Find the GCF of 10 and 25 by Long Division Method?

To find the GCF of 10, 25 using long division method, 25 is divided by 10. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 10, 25?

The following equation can be used to express the relation between LCM and GCF of 10 and 25, i.e. GCF × LCM = 10 × 25.

What are the Methods to Find GCF of 10 and 25?

There are three commonly used methods to find the GCF of 10 and 25.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 25 and 10 is 5, Find its LCM.

GCF(25, 10) × LCM(25, 10) = 25 × 10
Since the GCF of 25 and 10 = 5
⇒ 5 × LCM(25, 10) = 250
Therefore, LCM = 50
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